Benefit Transfer for Resource Valuation Econometric Considerations and a NV Case Study

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Benefit Transfer for Resource Valuation
Econometric Considerations and a NV Case Study

• Klaus Moeltner
• University of Nevada, Reno

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Outline

• The Concept of Benefit Transfer (BT)
• Start NV Case Study
• Types of BT
• Future Outlook
• Econometric Challenges
• N vs. K
• Optimal Scope
• Small Samples (NV Case Study)
• Need for Interdisciplinary Work

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Benefit Transfer Definition
Non-Market Valuation
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Benefit Transfer Applications

• Air Quality Improvements Smith Huang (1995)
• Value of a Statistical Life Smith et al., 2006
• Water Quality Improvements Iovanna Griffiths
  (2006)
• Marine Habitats Loomis (2006)
• Farmland Preservation Johnston (2007)
• Wetlands Moeltner Woodward (2007)
• Good Starting Point Special Issue of Ecological
  Economics (vol 60, 2006)

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BT NV Example
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Benefit Transfer Lit. Search
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BT Types Point Transfer
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BT Types Function Transfer
Individual Studys Regression Model
Attributes for Policy Site(Site
Characteristics,User Population)
Estimated Parameters
Benefit Estimatefor Policy Context
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Function Transfer Example
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BT Types Meta-Regression Model
Meta-Regression Model (MRM)
Attributes for Policy Site(Site
Characteristics,User Population)
Estimated Parameters
Benefit Estimatefor Policy Context
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Advantages of MRM for BT

• Represents prototypical context higher
  affinity with policy context than any single
  study
• Allows incorporation of site / context specific
  quality attributes
• Allows explicit control of study-methodological
  effects

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Benefit Transfer Outlook

• Regardless of the services and benefits being
  valued ..., EPA rarely conducts original
  valuation studies to support a proposed rule
  (Iovanna Griffith, 2006, p. 475)
• Original assessment studies will undoubtedly
  remain a rare exception (ibid, p. 476)

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Econometric Challenges

• N vs. K
• Optimal Scope
• Small Samples

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Econometric Challenges N vs. K
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Econometric Challenges N vs. K

• Option 1 Preserve N at cost of K
• Reduce set of explanatory variables for MRM and
  Benefit Transfer (BT) to a few regressors common
  to all sources
• Option 2 Preserve K at cost of N
• Keep a larger set of regressors and reduce the
  number of observations in MRM (boost K at cost of
  N)
• Compromise Use deficient data in Bayesian priors
• Moeltner et al., 2007

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N vs. K Bayesian Model
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N vs. K Refined Bayesian Model

• Step 1 Use basic model on deficient data
• Step 2 Use results from step 1 to construct
  refined priors

• Step 3 Estimate Bayesian model with main data
• and refined priors

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N vs. K Results
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Optimal Scope

• Tempting Augment MRM with activities / context
  that are similar or related to the policy
  application
• Broaden the definition of the dependent variable,
  i.e. the Scope of the MRM
• Ex Policy context WTP for day of trout fishing
• Augment with bass fishing?
• Ex Policy context Benefits of SO2 reduction
• Augment with NOx, COx reduction?

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Optimal Scope Example

• Starting point 1 Definition of policy context
• Here along 2 dimensions (discrete)
• Type of fishery Coldwater
• Type of environment Running water
• Starting point 2 What info is available for the
  policy context?
• Here (Targeted or expected) catch rate

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Example, contd
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Example, contd
Broaden Scope of MRM along dimension type of
fishery
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Model Space for Data Space 1
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Different Data Spaces

• D0baseline
• D1baseline, warmwater
• D2baseline, stillwater
• D3baseline, warmwater, stillwater
• Each data space has its own model space
• Each data space (likely) has a different sample
  size
• Each data space has to be examined for the most
  efficient model for BT

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Spacing Out
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The Classical Dilemma

• Battery of specification tests
• time consuming
• dependence on asymptotic test distributions
• risk of compounding decision errors
• ORForce pooling ex ante
• Risk of mis-specification bias
• OR Stick with baseline model
• Live with small sample problems and data gaps
• Solution Bayesian Model Search
• via Stochastic Search variable Selection (SSVS)

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How SSVS works
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Example of GS Sequence
Assume delta, and thus gamma, have 3 elements.
A GS series of 20 draws could look like this
11/20 0.55
4/20 0.20
Two key results flow from this output
1) How often , out of R draws, was a given
element of delta selected to be in the model-
shows relative importance of given regressor
2) How often each model is represented get
model weights
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General Estimation Process

• 1) Run kernel model with standardized regressors
  and SSVS, get model weights
• 2) Re-run each model w/o SSVS
• For each model, derive posterior distribution of
  BT predictions
• 3)Average predictions over models using weights
  from step (1)

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Augmentations

• Along 2 dimensions, as in initial example
• warmwater fisheries
• stillwater environment

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Augmentation with warmwater
Baseline results
Model-averaged predictions slightly more
efficient than baseline!
Means in same ballpark as baseline
Model weights null-heavy, rest diffuse
Stds slightly smaller less noise in augmented
models!
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NV Case Study Swamp Cedar NA

• 3200 acres
• Marshy ecosystem
• Globally unique stand of Swamp Cedars
  (Juniperus scopulorum)
• Access via dirt road
• Some recreational opportunities, but no
  infrastructure

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Shoshone Ponds Natural Area

• 1240 acres
• More Swamp Cedars
• Three man-made, spring-fed ponds that harbor two
  endangered fish species (Relict Dace, Pahrump
  Poolfish)
• Designated access road
• Some recreational opportunities, but no
  infrastructure
• Some educational opportunities (visiting school
  classes etc)

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Source Studies for MRM

• Initial Criteria
• Geographic area U.S. or Canada
• No coastal / marine types of wetlands
• Economic values must include habitat,
  biodiversity, or species preservation
• No studies with sole purpose of flood control,
  water filtration, extractive use
• First cut 24 studies
• Further refinements
• Eliminate studies with identical survey
  instruments and target population
• Eliminate if response rates lt30 (only 1)
• Left with 9 studies, 12 observations

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Choice of Regressors for MRM

• Based on
• Whats know for policy site
• Whats available from source studies / census
• Sample size 3 or 4 regressors at most
• Adj. R2 from prelim. OLS runs
• Final set
• Income (census info for policy site)
• Percentage of users (educated guess for policy
  site)
• Acreage (known for policy site)

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Meta-sample Stats
Simple mean transfer implausible
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Classical Estimation Issues

• Cant invoke asymptotics
• Cant test for HSK or other specification issues
• Robust s.e.s meaningless
• Conversion from log(WTP) to WTP problematic!
• Confidence Intervals for BT estimate cant be
  trusted
• Cant exploit extraneous info beyond data set

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Bayesian Approach

• Does not rely on asymptotics
• Can model HSK with a hierarchical error structure
  and a single added parameter
• Can introduce added info through refinement of
  priors
• Each model receives a probability weight as
  by-product of posterior simulator
• This allows for model-averaged BT predictions

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Model Fit and Weights
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Benefit Transfer Results
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Need for Interdisciplinary Work

• Get maximum info for policy context and existing
  studies
• GIS
• Satellite Images
• Example Troy Wilson (2006)
• Need for realistic scientific scenarios of policy
  impact
• Wetlands gone in 2 years or 20 years?
• Speed / nature of transition stages
• Time-dependent BT

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Parking Lot

• Just some ancillary stuff that might me useful
  for the QA phase of the presentation

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Kernel MRM
Gewekes (1993) t-error model
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Likelihood Function
Called Data Augmentation in Bayesian Jargon
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Priors
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Estimation

• Posterior Simulator based on Gibbs Sampler
• v-term requires Metropolis-Hastings within
  Gibbs
• Things to watch for
• MH acceptance probability (44 ideal)
• Convergence of simulator (use Gewekes 1993
  diagnostics tools)
• Choice of mixture variances not too close, not
  too far apart

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Closer look at Predictions
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Augmentation with stillwater
Baseline results
Model-averaged predictions less efficient than
baseline!
Means higher than baseline
Model weights null-heavy, rest diffuse
Stds larger more noise in augmented models!
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Interpretation of Results

• In terms of underlying preferences, warmwater
  fishing at running water appears to be more
  closely related to baseline activity than
  coldwater fishing at stillwater.
• Augmentation with warmwater increased sample
  size by 29, of included studies by 40
• Model-averaged augmented predictions more
  efficient, more representative (due to larger
  number of underlying studies)

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Kernel Model
Gewekes (1993) t-error model
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Model Space
Plus same 12 models with normal errors, for a
total of 24 models considered
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Priors and Refinements
Reasonable starting point
Using info on slope estimates from source studies
and other meta-analyses
Based on preliminary OLS results